# A class of non-algebraic threefolds

Annales de l'institut Fourier (1989)

- Volume: 39, Issue: 1, page 239-250
- ISSN: 0373-0956

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topToma, Matei. "A class of non-algebraic threefolds." Annales de l'institut Fourier 39.1 (1989): 239-250. <http://eudml.org/doc/74828>.

@article{Toma1989,

abstract = {Let $X$ be a compact complex nonsingular surface without curves, and $E$ a holomorphic vector bundle of rank 2 on $X$. It turns out that the associated projective bundle $\{\bf P\}E$ has no divisors if and only if $E$ is “strongly” irreducible. Using the results concerning irreducible bundles of [Banica-Le Potier, J. Crelle, 378 (1987), 1-31] and [Elencwajg- Forster, Annales Inst. Fourier, 32-4 (1982), 25-51] we give a proof of existence for bundles which are strongly irreducible.},

author = {Toma, Matei},

journal = {Annales de l'institut Fourier},

keywords = {compact complex surface; non-algebraic surface; complex threefold; holomorphic vector bundle; strongly irreducible bundles},

language = {eng},

number = {1},

pages = {239-250},

publisher = {Association des Annales de l'Institut Fourier},

title = {A class of non-algebraic threefolds},

url = {http://eudml.org/doc/74828},

volume = {39},

year = {1989},

}

TY - JOUR

AU - Toma, Matei

TI - A class of non-algebraic threefolds

JO - Annales de l'institut Fourier

PY - 1989

PB - Association des Annales de l'Institut Fourier

VL - 39

IS - 1

SP - 239

EP - 250

AB - Let $X$ be a compact complex nonsingular surface without curves, and $E$ a holomorphic vector bundle of rank 2 on $X$. It turns out that the associated projective bundle ${\bf P}E$ has no divisors if and only if $E$ is “strongly” irreducible. Using the results concerning irreducible bundles of [Banica-Le Potier, J. Crelle, 378 (1987), 1-31] and [Elencwajg- Forster, Annales Inst. Fourier, 32-4 (1982), 25-51] we give a proof of existence for bundles which are strongly irreducible.

LA - eng

KW - compact complex surface; non-algebraic surface; complex threefold; holomorphic vector bundle; strongly irreducible bundles

UR - http://eudml.org/doc/74828

ER -

## References

top- [1] C. BᾸNICᾸ & J. LE POTIER, Sur l'existence des fibrés vectoriels holomorphes sur les surfaces non-algébriques, J. reine angew. Math., 378 (1987), 1-31. Zbl0624.32017MR89h:32054
- [2] W. BARTH, C. PETERS & A. VAN DE VEN, Compact complex surfaces, Berlin-Heidelberg-New York, 1984. Zbl0718.14023MR86c:32026
- [3] G. ELENCWAJG & O. FORSTER, Vector bundles on manifolds without divisors and a theorem on deformations, Ann. Inst. Fourier, 32-4 (1982), 25-51. Zbl0488.32012MR84f:32035
- [4] G. FISCHER, Complex Analytic Geometry, LNM 538, Berlin-Heidelberg-New York, 1976. Zbl0343.32002MR55 #3291
- [5] H. GRAUERT & R. REMMERT, Coherent analytic sheaves, Berlin-Heidelberg-New-York, 1984. Zbl0537.32001MR86a:32001
- [6] D. MUMFORD, Abelian varieties, Oxford Univ. Press, 1970. Zbl0223.14022MR44 #219

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